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Find a witch. Beat her with a rope. Repeat.

The UI for feeding party members is a little unintuitive, you have to use the "feed this item to the NPC" button (the one with the cookie icon) instead of the "use item" button. 

Each goddess only has one quest. Latex is always alchemists and latex cubes, rope is always a giant animated rope, metal is always robots etc. They don't apply any bindings by default, but with Bound Crusader they'll pick 2-3 random restraints that are associated with that god (it's listed in the item descriptions).

You're overthinking weapon selection, just find any melee weapon that deals decent damage for a reasonable SP cost. Swords are the most efficient overall and spears have the most OP gimmick, but as long as you're not meleeing people with a bow or something you'll generally be fine. Unarmed is a last resort.

Don't worry about losing rep for killing enemies, if a faction starts out hostile they're probably going to stay that way.

Armor does reduce damage somewhat, but the real benefit is that each piece protects you against one binding attempt. All torso armor has some kind of downside, but skirts, pauldrons and leather gloves/boots are free. Yes it looks goofy, that's why there's a setting to hide your armor.

All attacks are dodgeable as long as you have room to maneuver. Pay attention to the warning boxes.

There is a pretty decent in-game tutorial, if you weren't aware. It's the leftmost portal in the starting area.

By drones, are you talking about the Ancient Guardians drones or the Nevermere drones? The ancient drones can be drawn out and picked off like any other enemy. Wolf drones are summons, meaning your main priority should be to snipe the summoner. If they summon too many, just run away until they start despawning. (That being said, it's usually easier to just avoid starting any fights with Nevermere in the first place.)

Your main income streams come from defeating enemies and selling their dropped loot, ransoming enemies gets you almost nothing and intentionally getting tied up is terribly inefficient (the items are usually locked). You don't really need to buy more than two or three lockpicks from the shop, you can get plenty just by looting the random shiny spots on the ground.

First off, it sounds like you're playing on hard difficulty settings with a lot of drawbacks.  Don't do that. The easy options are there for a reason.

As for actual tactics:
Try to pick off enemies from outside their detection range. Wizard is good for this, the starting passive ability lets you cast a free attack spell every 16 turns (or 10, if you spend one of your starting spell points to upgrade it). Failing that, try to lure them away from their groups and into an open space where you have room to dodge. I'd recommend buying a spear from the starting merchants, it makes things even easier by forcing enemies to use their ranged attacks (which can generally just be sidestepped) rather than their melee (which usually hits a 90-degree arc).

Attacks with dashed warning boxes have a warmup of one or more turns. A lot of enemies' default melee attack is to apply restraints, which always takes two turns and can usually be interrupted by hitting them. You can exploit this if you're caught in a tight space: approach an enemy so they try to bind you, hit them once, then step out of the danger zone to reset the warmup. Be warned that if you're wearing a harness, melee evasion gets a lot harder because humanoids can grab you as a free action.

If you do get a restraint on you, try to remove it ASAP even if it's a "non-binding" restraint like a collar. Most common arm/hand restraints can be struggled out of under the right conditions, and most other non-metallic gear is weak to cutting. Pay attention to the descriptions and struggle messages, the game usually tells you outright what each item is weak to. Also note that most restraints aren't actually locked when they're first applied, that's a separate action.

You should do every quest, they give great rewards and are one of the few reliable ways to boost goddess rep. If you do insist on using the Bound Crusader drawback, any particularly harsh restraints (arm/hand restraints, or anything from the cyber doll set) will be unequipped when the quest is completed.

Goddess rep can increase/decrease escape difficulty by a fair amount, so I'd advise against breaking orbs early on. You can instead get spell points by looting certain chests (look for the ones with blue circles on them) or as a quest reward.

Binding enemies is generally harder than killing them, and non-humanoid enemies are outright immune. Don't bother unless you intend to recruit them, or if you accidentally started a fight with a friendly faction and want to avoid the rep hit (just don't actually capture them).

If you get stuck in jail, you'll eventually get rescued unless you disabled it in the starting options.